How do I find global rotation values of a child object?
Add a Copy Rotation constraint to the object you want to rotate. In constraint panel, set Target to that child object;
After seeing it being aligned well, CtrlA >  Visual Transform;
Delete that constraint, since you don't need it anymore.




Edit:

If you just want to "know" the global rotation info, you can simply AltP > Clear and Keep Transformation, then you will see the visual rotation applied, which is the global rotation. After getting what you want, you can simply CtrlZ to undo.